heats of hydrogenation experimental and computational hydrogen thermochemistry of organic compounds

HEATS OF HYDROGENATION Experimental and Computational Hydrogen Thermochemistry of Organic Compounds Copyright © 2006 by World Scientific Publishing Co.. There is at present no critical

Computational Hydrogen Thermochemistry of Organic Compounds

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HEATS OF HYDROGENATION

Experimental and Computational Hydrogen Thermochemistry of Organic Compounds

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Scholar, Teacher, Friend

He maketh me to lie down in green pastures

Psalms 23

Hydrogen thermochemistry consists of obtaining useful thermodynamic information by measuring the heat output upon adding hydrogen across the double or triple bond or bonds of an unsaturated organic molecule Though far less general in its application than combustion thermochemistry, it is simpler and it produces results of comparable accuracy Heats of hydrogenation constitute a body of thermochemical information that has had a historical significance far out of proportion to the small number of research groups that have engaged in the work Early studies (1935-1939) by Kistiakowski and coworkers at Harvard produced some of the most widely quoted results in all of thermochemistry, among them the conjugation energy of 1,3-butadiene and the resonance energy of benzene After an initial, highly productive period, however, hydrogen thermochemistry was cut short by World War

II, and it languished until the late 1950s, largely because chemists favored the vastly more general competing method of oxygen bomb calorimetry

Recent highly accurate quantum mechanical calculations requiring reference standards of comparable accuracy and the economics of fuels and petrochemicals have brought hydrogen thermochemistry back into contemporary focus There is at present no critical survey of the scattered literature on experimental methods and results of hydrogen thermochemistry, or the burgeoning field of computational hydrogen thermochemistry This short monograph is intended to fill that gap It is divided into three chapters, each covering a distinct part of hydrogen thermochemistry:

1 Practical and historical aspects of experimental determination of the

enthalpies of hydrogenation and formation \ydH29S and Af H29i of organic compounds, primarily hydrocarbons, are given in Chapter 1

2 Chapter 2 consists of a large table containing more than 500 Ah dH29S

values measured over 70 years of research, now scattered throughout the literature in English and in German One of the unusual aspects of this literature is that contemporary experimental advances, though they have brought about an increase in sensitivity measured in orders

of magnitude, they have not brought about a significant change in accuracy Thus the older literature contains results that are as valuable today as they were when they were first published Like all literatures, however, the hydrogen thermochemical literature varies in accuracy and reliability, both of which are commented upon within this table

3 Contemporary advances in computer hardware and software have brought about a immense increase in our ability to calculate (as distinct from measuring) Ahyd//298 Modern computational thermochemistry includes various empirical, semiempirical, and quantum mechanical methods for calculating Ah dHm of linear and cyclic alkenes, polyalkenes, alkynes and polyalkynes There is at present no critical survey of computational methods for determining

Ahyd//298 which Chapter 3 supplies

Whatever technological problems and successes the future may bring, we can be assured that they will be within the framework of classical thermodynamics

The author wishes to acknowledge the help and encouragement of colleagues and friends Joel Liebman, Nikita Matsunaga, and Andreas Zavitsas As always, I express my thanks to Tony Zeru Li for extracting

me from the computational problems I have created for myself in writing this book

1.3.1 Correction to the gaseous state 12

3.6.1 The Huckel method 176

3.6.2 Higher semiempirical methods 181

ix

3.7 Ab initio Methods 182

3.7.1 The Gaussian basis set 183

3.7.2 Post Hartree-Fock methods 185

3.7.3 Combined or scripted methods 186

3.7.4 Finding A(H29i and \yiHm from G3(MP2)

3.7.9 Complete basis set extrapolations (CBS) 201

3.7.10 Bond dissociation energies 202

Bibliography 207 Index 219

Hydrogen Thermochemistry

Historically, experimental heats of hydrogenation have had an importance far out of proportion to the small number of research groups engaged in their measurement Much of our quantitative understanding

of such concepts as resonance, conjugation, aromaticity and antiaromaticity, molecular strain, and the more subtle aspects of molecular stability arose from hydrogenation experiments For examples from the work of the six principal research groups in the field, see Conant and Kistiakowsky (1937), Williams (1942), Skinner (1959),

Turner et al (1973), Roth et al (1991), and Rogers et al (1998)

at constant pressure, the heat out is equal and opposite to the enthalpy

change of the system AH From the vast field of hydrogenation

chemistry, we shall concentrate almost exclusively on the thermochemistry of simple hydrogen addition to unsaturated hydrocarbons in this work Hydrogenation of unsaturated hydrocarbons always gives off heat, hence the molar enthalpy change of hydrogenation

Ahyd//298 is always negative

1

The molar enthalpy of formation A{H of any substance is the

change in enthalpy that takes place when elements combine to form one

mol of that substance by a formation reaction, real or hypothetical

Elements —> Compound

In the case of hydrocarbons, the formation reaction is

It is possible to determine the energy change of any well defined

chemical reaction AtU carried out at constant volume by measuring the

heat given off to or absorbed from the surroundings by suitable

calorimetric means (Heat absorbed increases the energy of the system

making ArU positive.) If a substance is burned at constant volume V,

one speaks of its "heat" of combustion ACU and if a hydrogenation is

run at constant pressure P, one speaks of its heat of hydrogenation,

meaning its Ah d//2 9 8 Energy and enthalpy are related by the

well-known definition H = U + PV

If the reactants and products of a formation reaction are in their

standard states, the enthalpy change is a standard enthalpy of formation

Afr/29g

mC(gr) + -H2(g,/> = 0.1 MPa) ->CmHn (stable form) (1.2)

where (gr) designates the graphitic form of carbon and the stable form of

the hydrocarbon is a gas (g), liquid (1) or a solid (s) according to the

temperature The unit of pressure is the pascal Pa = Nm'2, where 105 Pa =

1 bar = 1 atmosphere If the reaction is carried out at or corrected to a

standard temperature of 298 K (strictly defined as 298.15 K) the symbol

Af//298 is use<^- See Klotz and Rosenberg (2000), especially Table 4.1

for a more detailed discussion of standard states An enthalpy change

measured at or corrected to 298 K but not under strict standard state

conditions is denoted A//298 Each enthalpy change, Af//29gand

Ahyd//298, is a special case of the less restricted AH29i

A reliable Ah dH29i and a reliable enthalpy of formation Af//298 of

either the reactant or the product of hydrogenation leads to Af//29g of the

other participant in the reaction because A{H°(H2) - 0 at 298 K and 105

Pa by definition

AM^29g = Af ^298 (product) - Af H29i (reactant)

0

Frequently, the A{H29i of an alkane is accurately known but Af//29g

values of one or more of the several alkenes or alkynes that can be

hydrogenated to it are not known The hydrogenation experiment then

yields Af//298 (alkene or alkyne)by Eq (1.3) A simple example is that

of the isomeric linear hexenes, hexadienes, and 1,3,5-hexatriene, all of

which can be hydrogenated to give «-hexane Conditions are usually

such that AfH calculated from hydrogenation data is very close to the

enthalpy of formation of the alkene in the standard state A{Hl9i A less

usual situation is determination of the AfH29i of the product alkane by

combining AhdH29S with the known AfH29i of an alkene

Partial heats of hydrogenation that are not directly measurable can be

obtained from total heats of hydrogenation by an indirect calculation

H, 1,3-butadiene 1-butene (1.4) The hydrogenation of 1,3-butadiene to 1-butene cannot be carried out

quantitatively but we know the total heats of hydrogenation at 355 K of

both components to give ^-butane as the product (Conant and

-26.8 /

-30.3

Fig 1.1 A thermochemical cycle of hydrogenation reactions

These results (both in kcal mol"1, Chap 2) permit one to construct a thermochemical cycle with one unknown Ah dH , shown in Fig 1.1 as a

dashed arrow By the first law of thermodynamics, the closed path

around the cycle has AH = 0 , so

Ah y d#3 5 5(l,3-butadiene) = -57.1 - ( - 3 0 3 ) = -26.8 kcal mol"1 (1.6)

It is not always necessary to have an accurate AfH29S for the product alkane For example, if the Af i/2 9 8 (alkane) in Fig 1.1 were unknown or thought to be unreliable, calculation of Af//2 9 g (1,3- butadiene) and Af//2 9 8 (1-butene) would be suspect but Ah d//2 9 g of the difference between them, which is the partial reaction of 1,3-butadiene to 1-butene, would still be valid In this way Kistiakowsky (Conant and

Kistiakowsky, 1937) found the enthalpy of isomerization of cis- to 2-butene to be negative {trans more stable than cis) and to have AisomHi55 = - 0 9 5 ± 0 1 4 kcal mol"1 See also Turner and Garner (1957)

trans-for an analogous determination of the enthalpy difference between and endo-cyclic double bonds

exo-No one has ever claimed that hydrogen thermochemistry will replace combustion thermochemistry but, as Kistiakowsky pointed out in his first

paper on the subject (Kistiakowsky et al., 1935), reaction

thermo-chemistry, despite its lack of generality, is a powerful tool because it can

be expected to yield more accurate enthalpies of formation than combustion thermochemistry for some molecules under some circumstances Reaction thermochemistry, especially hydrogen

-57.1

thermochemistry, is particularly well suited for determination of small energy differences between large molecules

Hydrogenation thermochemistry has been effective in quantitative evaluation of quantum mechanical effects and molecular strain, for example, resonance stabilization of aromatic compounds, conjugative

stabilization of linear polyenes and polyynes, and steric effects in and trans- isomers Kistiakowsky's measurement of AhydH of benzene

cis-(Conant and Kistiakowsky, 1937) gave the first experimental, quantitative value of the resonance energy of benzene, long known qualitatively through its reluctance to add bromine across the presumed double bonds of its Kekule structure, and given a quantum mechanical rationale by Huckel in 1931 and by Pauling in 1933 The first quantitative measure of conjugation, hyperconjugation, and strain in organic molecules arose from Kistiakowsky's determination of the differences in Ahyd// among alkenes and between monoalkenes and dienes (Conant and Kistiakowsky, 1937)

Recent advances in computational chemistry have made it possible

to calculate enthalpies of formation from quantum mechanical first principles for rather large unsaturated molecules, some of which are outside the practical range of combustion thermochemistry Quantum mechanical calculations of molecular thermochemical properties are, of necessity, approximate Composite quantum mechanical procedures may employ approximations at each of several computational steps and may have an empirical factor to correct for the cumulative error Approximate methods are useful only insofar as the error due to the various approximations is known within narrow limits Error due to approximation is determined by comparison with a "known" value, but the question of the accuracy of the "known" value immediately arises because the uncertainty of the comparison is determined by the combined uncertainty of the approximate quantum mechanical result and the standard to which it is compared

Once the validity of a quantum mechanical procedure has been

established by its ability to reproduce various accurate experimental

results, the way is clear to calculate unknown thermochemical values of unstable or explosive compounds, unsuited to classical thermochemical methods, or to calculate thermochemical properties of molecules, radicals, or ions of fleeting existence (e.g., Zavitsas, Matsunaga, and

Rogers, 2005) Herein lies a major advantage of the accuracy inherent hydrogen thermochemical results and a reason for renewed interest in the diverse but scattered literature devoted to hydrogen thermochemistry Parts 1 and 2 of this work are devoted to experimental hydrogen thermochemistry while part 3 treats the emerging field of computational hydrogenation thermochemistry

1.2 History

In 1935, Kistiakowsky's group (Kistiakowsky et al, 1935) published the

first of a series of papers on the experimental determination of Ah H of

51 hydrocarbons containing from 2 to 10 carbon atoms They pointed out that, while experimental measurement of the energy of combustion

AcC/ is generally more precise than Ah H measurement, arriving at the

desired enthalpy of formation Af//29g, through Ah d//298 may be more

accurate because Ahyd//298 is much the smaller number Thus ACU

values increase monotonically with the number of carbons and the molecular weight but AhydH29S for monoalkenes, for example, do not

At the time of Kistiakowsky's first paper, many extant thermochemical results had been measured in the nineteenth century and are now of archival interest only Using these data, Kistiakowsky observed that it was impossible to calculate the magnitude or, in some cases, even the sign of energy differences resulting from small changes

in molecular structure This motivated an investigation into hydrogen thermochemistry by which the Kistiakowsky group determined Ahyd//298

at a level of precision of about ±0.1 kcal mol"1 For example, they found

Ahyd//298 for cis- and trans-2-butene to be -28.33 ±0.10 and

-27.38 ±0.10 kcal mol"1 respectively, leading to the isomerization enthalpy Aisom//298 - -0.95 ±0.14 kcal mol"1 and showing that the trans

isomer is the more stable of the two This was confirmed in 1951 by

accurate combustion thermochemistry Prosen, Maron et al found

AcH = -647.65 ±0.29 kcal mol"1 and AcH = -646.90 ±0.23 kcal mol"1 respectively, for the two isomers leading to Aisom//298 = -0.75 ±0.37 kcal mol"1, the difference between them Even in this simple case, the combustion results must be 28 times as precise as the hydrogenation results to achieve the same precision in the enthalpy difference A similar

calculation for Cg monoalkenes would require a precision ratio of 56:1, C12 requires a ratio of 84:1 and so on

The series of papers written by Kistiakowsky in the late 1930s is arguably the most influential group of research papers ever published on the relationship between experimental thermochemistry and molecular structure, for it contains the first quantitative assessment of the energetic influence conferred upon molecules by the structural features conjugation, hyperconjugation, aromatic resonance, and molecular strain Later, antiaromaticity and homoaromaticity were added to this list These structure-energy relationships are referred to directly or indirectly in most elementary organic chemistry textbooks to this day

Kistiakowsky's work was cut short by World War II, to be taken up briefly by Williams (1942), who carried out the first accurate Ahyd//29g

measurements made in solution Though the rationale of hydrogen

thermochemistry was investigation of relatively large molecules, the phase method used by Kistiakowsky had pretty nearly reached its limit in size because larger molecules are not volatile enough to be hydrogenated under the conditions he used The change-over from gas-phase thermochemistry to solution thermochemistry was inevitable if hydrogen thermochemistry was to move in the natural direction, that is, toward the study of larger molecules and molecules less volatile than hydrocarbons Solution hydrogenation does not suffer restrictions due to volatility and can be carried out, in principle, at any temperature As an added complication, however, solvent interactions with both reactant and product may influence the measured AhydH29g These influences were treated in detail by Williams (1942)

gas-Following Williams' work, Skinner's group published 3 papers in the late 1950's (Skinner, 1957) Skinner's work is noteworthy for its exploration of intramolecular energetic interactions of alkynes

Starting contemporaneously with Skinner, Turner's group (Turner

et al., 1957) published a much larger body of work ending in 1973

Turner's work produced a substantial amount of data on the relative

stability of isomers, for example, exo-endo isomers like

methyl-cyclopentene and methylenecyclopentane

More recent work in hydrogen thermochemistry has been by the groups of Roth (1983) and of Rogers (Bretschneider and Rogers, 1970) Typically, work of the Roth group is characterized by numerous

measurements on structurally interesting molecules, high accuracy (typically ±0.5 kJ = ±0.1 kcal mol"1), and careful correction for small residual solvent effects

The method we presently use (Caldwell et al, 1997, Rogers et al,

1998) is not as accurate as the best results obtained by the methods above, but it is very sensitive Within accuracy limits that are never better than + 0.8 kJ mol"1 = + 0.2 kcal mol"' (Rogers and Crooks, 1983) and may be as high as + 4 kJ mol"1, we can, in favorable cases, carry out

a complete series of AhydH29S determinations on a drop of liquid hydrocarbon Because the molecules one is most interested in are often

unstable, difficult to prepare, and difficult to purify (e.g., Rogers et al.,

1978), this can be a significant advantage

1.3 Theory and Methodology

Kistiakowsky's apparatus was a flow calorimeter A mixture of gaseous alkene or alkyne and hydrogen flowed into a reaction chamber filled with finely divided copper catalyst The reaction product plus heat flowed out of the chamber through a helical glass tube connected to a suitable collection device The purpose of the helical tube was to convey the heat of reaction to the calorimeter fluid in which the entire reaction system was immersed Upon reaching a steady state, the amount of heat produced per unit time was measured by the rise in temperature of the calorimeter fluid The amount of product alkane transferred to the collection device per unit time was also measured This gave the heat of reaction per mol of reaction product collected Calibration was by means

of a low-voltage electrical heating coil

Aside from its originality, Kistiakowsky's work is especially impressive in his anticipation of error sources and experimental problems and in the ingenious methods he used to circumvent them or to demonstrate that they had a negligible effect on the final result In their first paper, the Kistiakowsky group reported results for over 30 full hydrogenation experiments on ethylene Their final average was

Ah d//3855 =-32.824 ±0.050 kcal mol"1, where the notation designates reactants and products in the gaseous state at 355 K, reported by Kistiakowsky as 82° C Kistiakowsky also calculated Ah dH^ =

-31.000 + 0.150, Ahyd//2873=-32.460 ±0.050, and A ^ , =

-32.575 ±0.050 ±0.050

Almost all of Kistiakowsky's further studies were carried out at

355 K and some concern has been expressed in the literature that the

difference between Ahyd//355 and Ah d//298 might invalidate or at least

diminish the usefulness of his results This difference appears to be quite

small, however The change in constant pressure heat capacity, ACP, for

a reacting system

consists of the difference in Cp for the alkane and that of the alkene plus

Cp(hi2) The CP difference between two hydrocarbons is generally

quite small, that of the alkene being slightly less than that of the alkane

The difference is partly made up by CP(H2), so the change in heat

capacity brought about by going from the reactant system to the product

is small and the change in enthalpy of reaction with temperature is

correspondingly small The ACPAT contribution to AhydH29S over the

temperature range specified is probably not larger than 0.25 kcal mol"1

(1.0 kJ mol"') per mole of hydrogen consumed in reaction 1.7 This

upper limit is calculable from the ethylene data above, because the

difference in Cp is larger for the ethylene-ethane pair than it is for the

other hydrocarbon pairs studied by the Kistiakowsky group

Williams (1942) gave details of the design of the first hydrogen

calorimeter constructed specifically for measurements of Ah dH302 in

solution It was a fairly conventional reaction calorimeter in which the

reaction took place in a Dewar flask, but it was made more complicated

by the necessity of maintaining the entire system under hydrogen-tight

conditions The sample was contained in a glass ampoule broken by an

externally controlled mechanical device to initiate the reaction The

temperature was 302 K, negligibly different as far as this work is

concerned from 298 K Difficulties with different choices of solvent and

catalyst were discussed and eventually glacial acetic acid and Pd were

selected We shall discuss solvent effects in Sec 1.3.1

The design used by Skinner's group entailed a reaction vessel

agitated by vertical oscillation within a conventional Dewar flask

Reaction times were 10-20 minutes as contrasted to several hours

reaction time in the Williams calorimeter The solvent was glacial acetic acid and the catalyst was reduced PtO Oscillatory calorimeters have not found favor since this work

Turner's calorimeter was a modification of the Williams design using rotary stirring and catalyst introduction into the reaction mixture

by breaking an ampoule Turner notes a discrepancy between his results and those of Kistiakowsky for the test compound 1-heptene but does not mention the solvent effect Turner also points out that the discrepancy is larger for polyenes than it is for monoenes, becoming quite substantial,

viz 2.3 kcal mol"1 in the case of cycloheptatriene Turner's group produced a large amount of excellent thermochemistry but it is regrettable that the solvent corrections necessary to convert their results

to the gas phase (see below) were not quantitatively accessed Careful measurements of solvent effects are a salient feature of Roth's hydrogenation studies described below

We noticed early in our study of hydrogenation thermochemistry (Rogers and McLafferty, 1971) that glacial acetic acid, the solvent of choice at that time, is not necessary to achieve a useful reaction rate for small samples in the presence of large amounts of activated catalyst We carried out our work using hydrocarbon solvents as the calorimeter fluid Hydrocarbon solvents show much reduced solvent effects and have the added advantage of lower heat capacity than acetic acid, thus amplifying

the thermal signal AT The sample, in the form of a dilute solution in the

same hydrocarbon as that chosen as the calorimeter fluid, was injected

by means of a microsyringe Very small samples and large amounts of activated catalyst in the reaction slurry reduced reaction times by 100 fold from the previous minimum to about 10-20 s With such short reaction times, we chose to operate our microcalorimeter in isoperibol mode, that is, we made no attempt to maintain strictly constant temperature except that conditions were manipulated such that the temperature drift before and after reaction was not steep Injection of a

sample caused a typical sigmoidal temperature vs time curve from

which the temperature rise for the reaction was interpolated in the usual way (Rogers and Sasiela, 1973) In later versions of the calorimeter, these curves were stored in microcomputer memory and interpolated digitally (Fang and Rogers, 1992) Calibration of the thermal rise and

conversion to conventional enthalpy units was by comparison to the thermal rise of a "known" such as 1-hexene or cyclohexene

In this method, corrections are not made for the transfer enthalpy from solution to the gaseous state on the ground that solute molecules in very dilute solution with a noninteracting solvent are essentially independent of one another and mimic the ideal gas state This assumption has been questioned but the results are confirmed by

meticulous combustion experiments where they exist (Steele et al, 2002) and by high level computational values (Rogers, et al., 2004)

Roth (1980) developed a hydrogenation method which also uses alkane solvents, thus minimizing solvent interaction His calorimeter is a very accurate commercial isothermal titration calorimeter (Christensen

et al., 1973) and in his initial paper, he compared results with literature

values for five olefins The reaction vessel was maintained at constant temperature before, during, and after addition of a titer of dilute olefin solution by means of a motor-driven precision microburet Constant temperature was maintained by means of a constant rate Peltier cooler operating in opposition to a variable heater The heater delivered a number of fixed energy pulses to the reaction vessel controlled by a circuit with a thermistor inside the vessel During the titration, heat generated or absorbed within the vessel disturbed the balance between the heating and cooling devices and the number of pulses delivered to the heater changed in response to the control circuit At the beginning of the titration, a sharp change in the number of pulses was recorded and at the end, a change in the opposite direction was recorded The size of the step function was proportional to the enthalpy change within the reaction chamber This was converted to conventional enthalpy units by calibration against the heat output from a "reference" resistance heater

An advantage of this ingenious arrangement is that optimum precision could be obtained by adjusting either the voltage to the reference heater

or the speed of the microburet so that the size of the hydrogenation or solution plateau (or depression) was equal to that of the reference plateau

In his initial paper, Roth used acetic acid, methanol, and cyclohexane

as solvents and Pd over carbon support, Pt/C, Pt, Pd/BaS04, and Pt02

He settled on Pd/C and cyclohexane as optimal Precision and agreement with Kistiakowsky's results were in the region of 0.1-0.2 kcal mol"1

1.3.1 Correction to the gaseous state

Most contemporary molecular mechanical or quantum mechanical

calculations give the properties of a single molecule isolated from all

others, that is, a molecule in the ideal gaseous state Over the years,

enthalpies of hydrogenation have been measured by several experimental

strategies using a variety of solvents Only Kistiakowsky's early work on

relatively small molecules involved hydrogenation in the gaseous phase

For reasons of limited vapor pressure of substances of current interest,

his methods are unlikely to be used again

Given that some sort of solution thermochemistry is necessary, one

must either make the corrections outlined by Williams (1942) and Fuchs

and Peacock (1979) or make use of uncorrected or partially corrected

data with an awareness of the enthalpic corrections that have been

where (g) denotes the gas phase, \ydH is the uncorrected enthalpy

of hydrogenation measured in solution, and AH(v —» S) is the

enthalpy of transfer from vapor to solvent

A / / ( v ^ S ) = Asoln//-AvapJrY (1.8) The influence of experimental strategy on the solvent correction is

seen by contrasting the experiments of Williams with those of Turner's

group Williams gives the equation

where L designates the molar "latent heats" of vaporization and solution

respectively, subscripted X denotes the reactant and Y denotes the product In the notation we use here, Lv = Avap/7 , Ls = Asoln// , and

Ahyd#298 (8) = Ahyd// ~ AvaP//298 (alkene) + Avap//298 (alkane)

-Asoln//298(alkane) (1.10)

for the reaction of a liquid alkene to the corresponding liquid alkane where the temperature is taken to be 298 K If the reactant and product are both solids, Williams's Eq 2 is, in our notation,

Ahyd#298 (g) = \yiH ~ Afus^298 (alkene) + A&s//298 (alkane)

- AvaP#298 (alkene) + A vap//298 (alkane) - Asoln//298 (alkane) (1.11)

where AfusH29S denotes the enthalpy of fusion of the solid at 298 K

As a trial case, Williams chose hydrogenation of 1-heptene He equilibrated Pt or Pd catalyst in glacial acetic acid under dry H2 at a pressure just over ambient Upon breaking an ampoule containing 1 to

1.5 g (accurately weighed) of 1-heptene, AhdH was measured for the

reaction

l-heptene(l) + H2(g) —> «-heptane (s)

where (1) denotes the liquid state and (s) denotes »-heptane in solution The temperature was 302.1 K Results using Pt catalyst took up more than one equivalent of H2 and were deemed unsuitable The result obtained for 3 runs using Pd catalyst was

AhydH = -28.280 ±0.127 kcal mol'1

The enthalpy of solution of «-heptane in glacial acetic acid was found in

a separate experiment to be 1.436 ±0.006 kcal mol"' Williams took enthalpies of vaporization from the literature, obtained by standard classical thermodynamic means, and corrected them to a temperature of

302.1 K to coincide with his AhydH measurements This led to a

difference

- Av a p#3 0 2, (1 -heptene) + Av a p//3 0 2, (rc-heptane) = -0.257 ± 0.152 kcal mol"1

The corrected Ahyd//298(g) is

Ahyd//298(g) = -28.280 ± 0 1 2 7 - 0.257 ± 0.152 -1.436 ± 0.006 kcal mol"1

which leads to Ah y d//3 0 2 1(g) = -29.973 ±0.255 kcal mol"1 This value was further corrected from 302.1 K to 355.1 K in order to coincide with Kistiakowsky's measurements The result was

Ahyd//355 ,(g) = -30.195 ±0.285 kcal mol"1

This is to be compared to Kistiakowsky's measurement of

Ah y d//3 5 5 1(g) = -30.137 ±0.037 kcal mol"1

Agreement is well within experimental uncertainty The uncertainty

in the difference between the two enthalpies of vaporization is largest and the enthalpies of vaporization contribute least to the result It is to be anticipated that these enthalpies will not be known for most compounds

of future interest, and the temperature at which these experiments were carried out, 302.1 K is closer to the temperature of interest, 298.1 K, so Williams simply dropped the vaporization and temperature corrections to obtain Ah d//3 0 2 ,(g) =-29.716±0.133 kcalmol" The precision of this measurement is about 0.5% or 0.15 kcal mol"1 He estimates the over-all uncertainty as ± 1.0% = 0.3 kcal mol"1

Turner's experimental strategy leads to a slightly different correction pattern In a slight variation in procedure, Turner's group broke the sample ampoule before a similar catalyst ampoule They re-equilibrated the system before breaking the catalyst ampoule and measured the temperature change The heat of activation of the catalyst, measured in a separate experiment, was subtracted from the total measured heat In this way, the liquid —> solution reaction of Williams was replaced by a solution —> solution reaction, partly escaping the thermal effects of

dissolution of the liquid or solid sample, hence partly escaping the necessity for their correction The escape was not complete however, because, during hydrogenation in glacial acetic acid, a fairly strong solvent-alkene complex is broken up with formation of a solvent-alkane complex which is weak if it exists at all Breaking up the complex is endothermic to the extent of about 0.7 kcal mol"1 per mole of H2, causing the measured Ahyd//298 to be 0.5 kcal mol"1 less exothermic than it would

be in the absence of a solvent effect

1.4 Accuracy

Literature values of \yAH19% are numerous and accurate There are about 500 known enthalpies of hydrogenation, but there has been no compilation of results since that of Jensen more than a quarter-century ago (Jensen, 1976)

Many of the Ah d//,98 values in the literature have an experimental uncertainty of 1 kJ mol or less For example, measurements of Ahydi/298 (1,3,5-cycloheptatriene) using three different techniques in experiments

separated by 44 years (Conn et ah, 1939, Turner et al, 1973, Roth et al,

1983), have an arithmetic mean experimental uncertainty and a range, when corrected for solvent effects and temperature differences to 298 K,

of 1.1 kJ mol This level of accuracy is important now that advances in computational methods are such that we may have to decide, between two computational methods that differ by 2 kJ mol , as to which is in

better agreement with experiment (Martin, 1998, Raghavachari et al,

1997) In matters of this kind, the old standard "thermochemical accuracy" of 1 kcal mol"1 (4.2 kJ mol ) no longer suffices AhydH values

are often accurate and precise enough to meet current stringent accuracy standards for use in evaluation and comparison of computational procedures, and for parameterization of empirical or semi-empirical

computational methods (e.g., Rogers et al., 1979)

1.5 Applications

A simple determination of resonance stabilization in benzene is shown in Fig 2 Suppose we take three moles of cyclohexene and one mole of benzene as two different thermodynamic systems, each having three

moles of double bonds Upon hydrogenation, the heat output is very different for the two systems The cyclohexene system suffers a decrease

of AhyiH29B= 3(-28.6) = -85.8 kcal mof'= -359 kJ mol"', while the

benzene system has Ahyd//298 of only -49.8 kcal mol = -208 kJ mol Benzene has a lower enthalpy than we might expect it to have and is said

to be more stable by 36 kcal mol = 151 kJ mol relative to 3 moles of

cyclohexene Stability in benzene is conventionally ascribed to

"resonance", a quantum mechanical property related to the release of spatial constraints on the electrons in benzene relative to those in cyclohexene, i.e., electron derealization

as distinct from things (ring currents, etc.) that we suppose are correlated

with enthalpy Theoretical artifacts ("hyperconjugation", "virtual states",

etc.) have the disadvantage that they can be molded to fit an author's

preconceived notions (e.g., Jarowski et al, 2004) Thermodynamic

numbers are what they are, impervious to argument Stability is, in the final analysis, a thermodynamic property

The thrust of much modern preparative chemistry is toward synthesis and purification of milligram amounts of product This has great advantage in making micro-purification methods feasible, often providing the experimental thermochemist with 99+ % samples of rare, often unstable compounds, albeit in very small amounts Synthetic virtuosity feeds the interest of theoretical chemists, but it places correspondingly great demands on the sensitivity of the thermochemical

methods to be employed in finding AhydH (or AcH ), and ultimately the

desired enthalpy of formation Af H29S

1.6 Details of Calorimeter Construction

Given the availability of modern instrumentation, the contemporary chemist is spared the meticulous and laborious procedures followed in

early hydrogen thermochemistry (see, for example, Kistiakowsky, et al.,

1935, 1936) Only two more recent hydrogen calorimeter tations are recommended to the scientist who wishes to pursue this line

implemen-of research, one a commercial instrument (Tronac Inc Orem , UT, USA) and one that can be constructed from standard laboratory equipment with

a few modifications

Roth's group has achieved excellent results using a commercial,

electrically calibrated, titration calorimeter (Roth, et al, 1980 and

following papers) Some of the instrumental details of the calorimeter

have been reviewed (Christensen, et al, 1973) along with details of its

testing on standard substances (Roth and Lennartz, 1980) In this work,

the measured enthalpy of solution of, for example, isooctane in

cyclohexane becomes smaller during a titration run owing to the change

in the nature of the cyclohexane-isooctane mixture as isooctane is added This nearly linear change was extrapolated to the "first" solution enthalpy, that is, As o | n// at infinite dilution A comparable trend in

AhydH during the during sample addition was not observed

Because the commercial instrument used by Roth has been fully

documented (Christensen et al., 1973), the "home made" device will be

more completely described here We have constructed calorimeters from

a design that has evolved with use over a number of years (Rogers, et al,

1971 and following papers), Throughout the evolution of the design, principles of simplicity, economy, miniaturization, and, above all, safety have been followed Simplicity, economy, and safety need no recommendation The categories given are not mutually exclusive For example, the smaller the calorimeter and its attendant hydrogen carrying apparatus, the less hydrogen there is to be controlled, the less hydrogen that will escape in the event of an accident, and the safer the entire procedure is In 30 years of hydrogenation research, we have suffered no injuries

Miniaturization is especially advantageous in an era when compounds with extraordinarily interesting structural and thermo- chemical properties are being synthesized but only in very small amounts Because the first principle of all calorimetry is that the sample must be well defined and pure (or at least have a small amount of known impurity), microcalorimetry permits use of a wider range of contemporary purification techniques, especially preparative gas chromatography, than traditional calorimetry There is, of course, no reason to suppose that the evolutionary process of hydrogen calorimeter design cannot be continued to produce smaller, safer, and possibly more accurate instruments

The calorimeter used in our laboratory was a 25 ml Erlenmeyer flask sealed by means of a serum stopper (Z 10,076-5, Aldrich Chem Co.,

P O Box 2060, Milwaukee, Wisconsin 53201, USA) containing about

10 ml of a stirred slurry of catalyst and a noninteracting, nonpolar solvent, typically «-hexane, but possibly one of many other choices, as the occasion demanded

an ordinary dry cell, the output of which was fed into a millivolt recorder (Rogers, 1980) Injection of sample or standard causes a rapid reaction in the flask at the left of the schematic diagram in Fig 1.3, which brings about a change in the resistance of the thermistor and a change in the voltage output of the bridge

The catalyst charge was 200-300 mg of 5% or 10% Pd or Pt on charcoal (Aldrich) Stirring rates of approximately 400-600 rpm were used (Multistirrer 6 or equivalent, www.velp.com ) The exact stirring rate is flexible but it must be held constant during a run to achieve a moderate, steady temperature drift before and after the temperature rise due to hydrogenation The reaction flask, wrapped in an insulating blanket, was firmly held in place by a styrofoam box or plain 600 mL beaker glued to the upper surface of the stirrer so that only the inlet septum protruded slightly from the insulation In constructing the box, the walls should be thick but the bottom should be thin or there should be

no bottom at all in order not to interfere with stirring This, of course, requires a stirrer that produces very little heat during constant operation over the entire experiment

Hydrogen was admitted to the reaction flask by means of a hypodermic needle thrust through the septum of the serum stopper Upon admission of hydrogen, a sharp temperature rise of several mK occurs due to activation of the catalyst After a few minutes, the temperature begins to drift slowly down The calorimeter is ready for the first injections of sample and standard when the temperature drift as seen on the recorder or microcomputer monitor (see below) approximates the drift lines in Fig 1.5 Over a time span of 10-30 s, the drift should be well approximated by a linear function

The Tygon tube connecting the needle to the hydrogen source should

be of as small bore as possible and should be as short as possible Although we did not use it, if we were to build another hydrogen calorimeter, capillary tubing would be used throughout in order to keep the volume of hydrogen small Lecture bottles of hydrogen are available ( sigmaaldrich.com CAS#295396-56L) Under an internal operating pressure of ~1 atm over ambient pressure, the stopper sometimes pops out This can be prevented by a drop of "Krazy Glue ®" (Elmer's

Products Inc Columbus OH 63215-3799) Safety precaution: The

stopper must be forced very firmly into the mouth of the flask Always wrap the flask in a towel or wear protective gloves to prevent cuts in case the flask breaks

Samples consisting of 20-40 uL of an approximately 10% solution (depending on the degree of unsaturation) were injected through the septum using a 25 or 50 uL microsyringe fitted with a KelF adaptor (Hamilton Co P O Box 10030, Reno, Nevada 89510, USA)

Determination of Ahyd//298 of an unknown alkene or alkyne was by comparison with that of a standard, usually Ah d//29g(l-hexene) = -30.25 kcal mol"' (Skinner and Snelson, 1959, Rogers, 1979) Injections

of sample were made in alternation with injections of the standard in order to measure the ratio of output heats ^(sample) / ^(standard) Waiting a few moments between injections was sufficient to reestablish a baseline as in Fig 1.5 Statistical analysis shows that 9 ratios (18 injections in all) are optimum in order to take enough samples for statistical validity of the 95% confidence limit calculation but to avoid needless and redundant measurements

The heat output of the standard, ^(standard) was adjusted to within a few % of the heat output of the unknown sample g(sample) by selecting the concentration of the standard solution Most of the time, g(sample) could be guessed fairly closely from that of analogous cases, enabling us

to select the right concentration of the standard solution at the outset If the first guess was wrong, results from the first few injections enabled us

to calculate the right concentration for the standard A new standard solution was made up to take the 9 ratio measurements necessary to complete the experiment

Once g(sample) = ^(standard), one already knows Ah d//298 of the sample to within a few percent The rest of the experiment is devoted to reducing this uncertainty as much as possible through the simple ratio

Ahyd//298 (sample) ^ g(sample) 30.25 g(standard) ' Given the calorimeter dimensions and standard and sample concentrations above, the voltage output of the bridge was 1-2 mv Rise time of the voltage from a steady drift before reaction to a steady drift

after reaction was 10-12 s Temperature changes were not calculated; only the ratio of the heats in Eq (1.12) was needed Voltage output from the bridge can be input to a potentiometric recorder so as to obtain pairs

of standard-sample reactions which give response curves like those in Fig 1.5 Fitting a pair of verticals to the extrapolated linear drifts before and after reaction for a series of 18 alternating injections of standard and sample leads to a series of 9 ratios of verticals which is the series of

^(sample) /g(standard) ratios we seek for 9 replicate solutions of

Eq (1.12) Calculation of the mean, standard error, and standard deviation follow routinely

1.7 Design Modifications

We used either a commercial Wheatstone bridge or one of several that were easily assembled on a circuit board from commonly available parts Working from recorder output is inconvenient, and in some case subjective (as in where, exactly, to draw the vertical when you know the result you want) For this reason we substituted the A-D converter and microcomputer in Fig 1.4 for the recorder

The topic of computer interfacing is a large and changing one An early and very readable introduction to the field was given in the

Bugbooks by Larsen (1975) and Rony (1976), who were active at the

very beginning of the microcomputer revolution More recently, An (1998) has reviewed the subject

P"0 [] flD

INJ BR A-D COMP PRN

Fig 1.4 Schematic diagram of the calorimeter with an interfaced computer

Typically, the bridge output was conveyed through an A-D converter

to the computer COMP, where several hundred points on the curve were stored digitally and the curve was displayed on the computer monitor Operational amplifiers were also used between the bridge and A-D

converter with satisfactory results Depending on the converter properties, the amplifier may or may not be necessary

The computer was programmed to perform a linear least squares fit

to the temperature drift before and after reaction to give the equation of the upper and lower straight lines in Fig 1.5 The difference between the two linear least squares functions at the vertical passing through the point 2/3 up the reaction thermogram (Rogers and Dejroongruang, 1988)

is proportional to the heat of reaction

Fig 1.5 Thermogram with least squares extrapolations

Alternating sample and standard injections, having previously input the Ahyd//298 of the standard to the computer, the computer carried out a simple arithmetic program to calculate

^(sample)/^(standard) and hence Ahyd//298 by Eq (1.12) The result was stored digitally, and printed out to PRN to obtain a hard copy record

Experimental Results

2.1 Enthalpies of Hydrogenation

Experimental uncertainties are in parentheses Some common names are

given In the annotated text, the symbol \ydH should be understood to

be a negative quantity and to refer to 298 K, unless otherwise stated

Table 2.1 Enthalpies of hydrogenation

Measurements of A hyi H by Kistiakowsky's group were made using a flow calorimeter

Reactants were in the gaseous state The temperature was usually, but not always, 355 K

Conn, J B.; Kistiakowsky, G B.; Smith, E A J Amer Chem Soc 1939, 61,

1868-1876 Temperature correction to 298 K was made by Cox, J D.; Pilcher, G., 1970

Thermochemistry of Organic and Organometallic Compounds Academic Press, New

York

23

Conn, J B.; Kistiakowsky, G B.; Smith, E A.J Amer Chem Soc 1939, 61, 1868- 876

The temperature correction to 298 K is probably about 0.4 kcal mol"1

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1936,55,146-153

<=3 H 6

(1) Propene

355 K 30.12(0.1) 126.0(0.1)

Hydrogenation was carried out in the gaseous phase

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1935, 57, 876-882

(1') Propene

298 K 29.85(0.05) 124.9(0.2)

Results are by indirect calculation from an equilibrium study The motivation for this

study was cross-checking the hydrogenation results The results are very slightly outside

of combined experimental error

Kistiakowsky, G B.; Nickle, A G Disc Faraday Soc 1951, 175-187

The difference between Ah d H (1,3-butadiene) and twice A h d H (1-butene),

2 ( - 3 0 3 4 ) - ( - 5 7 0 7 ) = - 3 6 kcal mol"1 = -15.1 kJ mol-1 is often called the

"conjugation stabilization energy" and is ascribed to derealization of electron

probability density in the diene

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

The internal double bond in 2-butene is stabilized by 2.7 kcal mol"1 = 11.3 kj mol"1

relative to the terminal double bond in 1 -butene

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1935, 57, 876-882

(3) 2-Butene, (Z)

cu-2-Butene

355 K 28.57(0.1) 119.5(0.1)

The difference in Ah d H between the E and Z isomers of 2-butene is the archetypal E-Z

isomerization energy, 1.0 kcal mol'1 = 4.2 kj mol"1 The E isomer is more stable than the

Z isomer, presumably due to methyl crowding in the latter

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1935, 57, 876-882

(4) Methylpropene

Isobutene

355 K 28.39(0.1) 118.8(0.3)

The difference in Ah ,H between 1-butene and methyl propene is often called a

"hyperconjugation energy", in this case, 2.0 kcal mol"1 = 8.2 kJ mol"1 In general, a methyl group alpha to a double bond is said to stabilize the reactant (See, however, e g.,

Rogers, D W Tetrahedron Letters 1987,28, 1967.)

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1935, 57, 876-882

C5H6

(1) Cyclopentadiene

355 K 50.86(0.2) 212.8(0.8)

The difference in Ah d H (cyclopentadiene) and twice A h d H (1-butene) is 9.8 kcal

mol"1 =41.1 kj mol"1 The enthalpy of the reactant state is lowered by conjugation and that of the product state is raised by hydrogen atom crowding in the 5-membered ring Both factors narrow the gap in enthalpy between reactant and product, which is Ah d H

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

Ah A H was measured in glacial acetic acid and corrected by a separate heat of solution

measurement The value given is for the liquid —> liquid reaction Experimental

uncertainty is large for alkynes and ene-ynes because experimental error increases linearly with Ahyd// The ene-yne conjugation stabilization relative to propyne and 2-butene is small, - 9 6 0 - ( - 9 7 3 ) = 1.3 kcal mol"1 = 5.4 kj mol"1, that is, \ yA H is

smaller in magnitude by this amount than it would be for a hypothetical molecule with no conjugation interaction

Skinner, H A.; Snelson A Trans Faraday Soc 1959, 55,404-407

(3) 3-Penten-l-yne, (Z)

c/s-Pent-3 -en-1 -yne

298 K 95.60(1.1) 400.0(4.6)

Ah A H was measured in ethanol and corrected by a separate heat of solution

measurement The value given is for the liquid —> liquid reaction It is noteworthy that

the E-Z stability ratio is opposite to that of the 2-butenes, suggesting that Z alkyne groups are less bulky than either Z methyl groups or H atoms The authors caution that the E-Z enthalpy difference is smaller than experimental uncertainty and that this conclusion should be regarded with some skepticism

Skinner, H A.; Snelson A Trans Faraday Soc 1959, 55,404-407

(2') 3-Penten-l-yne, (E)

298 K 97.0(0.3) 405.8(1.3)

Roth et al comment that thermochemical conjugation stabilization between the double bond and the triple bond is very much smaller than would be expected by analogy to 1,3-butadiene If Ah d H of an isolated terminal triple bond is taken as about -69.5 kcal

mol"1 and that of an internal double bond is ~ -28.0 kcal mol"1, the expected Ah A H of

a completely nonstabilized3-penten-\-yne, (E) would be -97.5 kcal mol"'

Roth, W R.; Adamczak, O.; Breuckman, R.; Lennartz, H.-W.; Boese, R Chem Ber

1991,724,2499-2521

(3') 3-Penten-l-yne, (Z)

c/i-3-penten-1 -yne

298 K 96.8(0.1) 405.0(0.4)

The more precise values 2' and 3' confirm the earlier conclusions 2 and 3

Roth, W R.; Adamczak, O.; Breuckman, R.; Lennartz, H.-W.; Boese, R Chem Ber

Roth, W R.; Klaerner F.-G.; Lennartz, H.-W Chem Ber 1980, 113, 1818-1829

mol"1 = —227.2 kJ mol"1, that is, for simple hydrocarbons, a rough kind of additivity is

observed Additivity rules will break down as more complicated cases are encountered later in this table

Dolliver, M A.; Gresham, T L.; Kistiakowsky, G B.; Vaughan, W E J Amer Chem

Soc 1937, 59, 831-841

(3) 1,4-Pentadiene

355 K 60.79(0.2) 254.3(0.6)

Ah & H for two terminal double bonds is within experimental uncertainty of twice the

value for the double bond in 1 -butene

Kistiakowsky, G B.; Ruhoff, J R.; Smith, H A.; Vaughan, W E J Amer Chem Soc

1936,55,146-153

(4) Cyclopentene

355 K 26.9(0.1) 112.6(0.4)

Ah A H of cyclopentene to produce cyclopentane is smaller than it is in cyclohexene

because of crowding of hydrogen atoms in the smaller product molecule relative to the larger one

Dolliver, M A.; Gresham, T L.; Kistiakowsky, G B.; Vaughan, W E J Amer Chem

Soc 1937,59, 831-841

(4') Cyclopentene

298 K 26.0(0.4) 109.0(1.8)

Ah ,H was measured in acetic acid solution Solvent effects for alkenes in this

experimental method cause the measured Ah d H to be very roughly 0.7 kcal mol"1 less exothermic than gas-phase values, which would lead to a corrected value of -26.74(0.44) kcal mol"1 = -111.9 kJ mol"1 This entry is the mean of 12 separate thermochemical experiments made over a 10-year period An extra digit is carried in the uncertainty when this measurement is used as an indicator of the overall uncertainty of the method

Turner, R B.; Jarrett, A D.; Goebel, P.; Mallon, B J J Amer Chem Soc 1973, 95,